beanpole family
n. A family whose living members come from many generations, but with few members in each generation.
Family relationships are expected to be dramatically altered by the ageing society. With people having fewer children and living longer, the whole notion of family will change. Widely extended families of cousins of similar age will be replaced by 'beanpole' families of many generations.
—Anthony Browne & Adam Blenford, “The British are getting steadily older. Hurray!,” The Observer, May 12, 2002
1987 (earliest)
The family unit, circa 1987, is a far different entity than it was in the 19th Century, Bengtson suggests. He speaks of "the rise of the verticalized family. We call it the beanpole family. It's becoming much higher and much skinnier." Whereas the family once encompassed cousins and second cousins and third cousins of perhaps two generations, now there are apt to be many living generations but few members of each generation interact.
—Beverly Beyette, “The importance of being family,” Los Angeles Times, November 03, 1987
A beanpole is a thin, straight stick that helps support a climbing bean plant. Since at least 1837 wisecrackers have used this term as a synonym for a lanky person. In the phrase beanpole family, it's used to contrast the standard image of a family's living members as a wide, bushy tree. Determinedly eschewing metaphor, many demographers prefer the term verticalized family, a phrase that appears in the earliest citation.